The membership form of an athlete graded in the following belts: grey, yellow, orange, green, blue, purple and brown must be signed by a black belt instructor who is certified by the IBJJF (with the exception of a few countries – fifth chapter)

The membership form of an athlete graded black belt must be signed by a black belt instructor no lower than 2nd degree who is certified by the IBJJF.

I know in Judo, you can only promote up to one rank below you. But I know some people who've recently been promoted to 1st degree BJJ Black Belt by other 1st degree Black Belts.

Is this legit??

Yes. In GB if the brown in question has met the usual time requirement or 18 months (not a hard rule but a guideline) then the 1st BB can ask if he can promote him through the GB HQ if they agree then the brown can be promoted to 1st by a 1st. I've seen this happen about 3 times now.

The membership form of an athlete graded in the following belts: grey, yellow, orange, green, blue, purple and brown must be signed by a black belt instructor who is certified by the IBJJF (with the exception of a few countries – fifth chapter)

The membership form of an athlete graded black belt must be signed by a black belt instructor no lower than 2nd degree who is certified by the IBJJF.